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10 CHAP TE R 1 0 DETERMINING SAMPLE SIZE AND THE SAMPLING METHOD A SURVEY THAT CHANGED SURVEY SAMPLING PRACTICE The Literary Digest, an influential general interest magazine started in 1890, correctly predicted several presidential campaigns by using surveys. The world was becoming accustomed to viewing surveys as accurate predictors of future events. But the predic- tion the magazine made in the 1936 election was so bad that it is given credit for not only Literary Digest’sfamous blunder was due to using a poor sampling method. causing the collapse of the magazine (it was purchased by Time in 1938) but for stirring interest in refining surveying sampling techniques. Alf Landon, the Republican candidate and Governor of Kansas was running against Democratic President Franklin D. Roosevelt. The Literary Digest used three lists as its sample frame for polling American voters. First, it sent a L E ARNI NG OBJ ECTI VE S ■ To become familiar with sample design terminology ■ To learn how to calculate sample size ■ To understand the difference between ―probability‖ and ―nonprobability‖ sampling methods ■ To become acquainted with the specifics of four probability and four nonprobability sampling techniques postcard to each of its two million subscribers. Secondly, it added to this sample with sample frames composed of lists of telephone owners and automobile owners. The Digest’ssurvey predicted Landon would win overwhelmingly. Roosevelt won in a landslide, taking 46 of 48 states. Only Maine and New Hampshire voted for Landon. What went wrong? The Literary Digesthad used an unusually large sample, yet the results were ter- ribly wrong. The answer: the sampling method was wrong. Remember, 1936 was the depths of the Great Depression. Those who could afford a magazine subscription, telephone, or automobile were much better off than the general public, and these ―better off‖ citizens were much more likely to vote Republican. So the Digestwas surveying, in very large num- bers, voters who were mostly Republican. They didn’t use a sampling method that would guarantee that Democratic voters would be just as likely to be surveyed. What this illustrates is that you must have a good sampling method. With a poor sampling method, even very large sample sizes will not produce good survey results. In contrast, other surveys using much smaller sample sizes predicted Roosevelt would win. They were ridiculed for using small samples, but their predictions were correct because they used sound sampling meth- ods. Among those producing accurate predictions was a young man named George Gallup. The Gallup Company exists today and is still conducting accurate surveys. In this chapter you will learn how the sample method is important in producing representative results, and how the sample size is important in producing accurate survey results.1 292 Chapter 10: Determining Sample Size and the Sampling Method ■ Where We Are: 1Establish the need for marketing research 2Define the problem 3Establish research objectives 4Determine research design 5Identify information types and sources 6Determine methods of accessing data 7Design data collection forms 8Determine sample plan and size 9Collect data 10Analyze data 11Prepare and present the final research report nternational markets are measured in hundreds of millions of people, national markets comprise millions of individuals, and even local markets may constitute hundreds of thousands of households. To obtain information from every single person in a market is usually impossible and obviously impractical. For these reasons, marketing researchers make use of a sample. This chapter describes how researchers go about deciding sample size and taking samples. We begin with defi- nitions of basic concepts such as population, sample, and census. To be sure, sam- ple size determination can be complicated,2but we describe a simple way to calcu- late the desired size of a sample and illustrate how the XL Data Analyst can be used to do these calculations for you. From here, we describe sample methods and dis- tinguish four types of probability sampling methods from four types of nonproba- bility sampling methods. Last, we present a step-by-step procedure for designing and taking a sample. BASIC CONCEPTS IN SAMPLES AND SAMPLING To begin, we acquaint you with some basic terminology used in sampling. The populationis the entire group under study as specified by the research project. For example, a researcher may specify a population as ―heads of households in those metropolitan areas served by Terminix who are responsible for insect pest control.‖ Asampleis a subset of the population that should represent that entire group. How large a sample and how to select the sample are the major topics of this chapter. A censusis defined as an accounting of everyone in the population. Of course, a sam- ple is used because a census is normally completely unobtainable due to time, accessibility issues, and cost. So, researchers must use samples that represent populations, which brings us to the accuracy concerns that always occur when a sample is taken. Sampling erroris any error in a survey that occurs because a sample is used. Sampling error is caused by two factors: (1)the method of sample selection and (2)the size of the sample. As for the latter, you will learn in this chapter that larger samples represent less sam- pling error than smaller samples, and that some sampling methods minimize this error, whereas others do not control it well at all regardless of the size of the sample. In order to select a sample, you will need a sample frame, which is some master list of all the members of the population. For instance, if a researcher had defined a population to be all shoe repair stores in the state of Montana, he or she would need a master listing of these stores as a frame from which to sample. Similarly, if the pop- ulation being researched consisted of all certified public accountants (CPAs) in the United States, a sample frame for this group would be needed. In the case of shoe repair stores, a list service such as American Business Lists, of Omaha, Nebraska, which has compiled its list of shoe repair stores from Yellow Pages listings, might be used. For CPAs, the researcher could use the list of members of the American Institute of Certified Public Accountants, located in New York City, which contains a listing of all accountants who have passed the CPA exam. As we all know, lists are not perfect representations of populations, because new members are added, old I ■ The population is the entire group under study as defined by research objectives. Determining Size of a Sample 293 While directories and phone books are readily available, they may have substantial sample frame error. ones drop off, and there may be clerical errors in the list. So, researchers understand thatsample frame error, be it great or small, exists for sample frames in the forms of mis-, over-, or underrepresentations of the true population in a sample frame. Whenever a sample is drawn, the amount of potential sample frame error should be judged by the researcher.3Sometimes the only available sample frame contains much potential sample frame error, but it is used due to the lack of any other sam- ple frame. It is a researcher’s responsibility to seek out a sample frame with the least amount of error at a reasonable cost. The researcher should also apprise the client of the degree of sample frame error involved. DETERMINING SIZE OF A SAMPLE Let’s just focus on the sample error associated with size of the sample. That is, for now, let’s assume that we can find a sample frame that has an acceptably low level of sample frame error, and that we can select a sample that is truly representative of the population. (We will take up sample selection methods after we discuss sample size.) The Accuracy of a Sample A convenient way4to describe the amount of sample error due to the size of the sample, or the accuracy of a sample, is to treat it as a plus-or-minus percentage value.5That is, we can say that a sample is accurate to ±x%, such as ±5% or ±10%. The interpretation of sample accuracy uses the following logic: If you use a sample size with an accuracy level of ±5%, when you analyze your survey’s findings, they will be about ±5% of what you would find if you performed a census. Let us give an example of this interpretation, as it is important that you understand how sample accuracy operates. We will take a sample that is representative of the population of people who bought birthday gifts in the past year, and let’s say that we find that 50% of our respondents say ―Yes‖ to the question ―The last time you bought a birth- day gift, did you pay more than $25?‖ With a sample accuracy of ±5%, we can say that if we took a census of the population of our birthday gift givers, the percent ■ Whenever a sample is taken, the survey will reflect sampling error. 294 Chapter 10: Determining Sample Size and the Sampling Method 16% A cc u ra cy Sample Size Sample Size and Accuracy From a sample size of 1,000 or more, very little gain in accuracy occurs, even with doubling the sample to 2,000. 14% 12% 10% 8% 6% 4% 2% 0% 50 200 350 500 650 800 950 2,000 1,850 1,700 1,550 1,400 1,250 1,100 Figure 10.1The Relationship Between Sample Size and Sample Accuracy ■ The accuracy of a sample can be expressed as a ±x% amount. that will say ―Yes‖ is between 45% and 55% (or 50% ±5%). Think, for a minute, about the incredible power of a sample: We can interview a subset of the entire pop- ulation, and we can extrapolate or generalize the sample’s findings to the popula- tion with a ±x% approximation of what we would find if we took all the time, energy, and expense to interview every single member of the population. The relationship between sample size and sample accuracy is presented graph- ically in Figure10.1. In this figure, sample error (accuracy) is listed on the vertical axis and sample size is noted on the horizontal one. The graph shows the accuracy levels of samples ranging in size from 50 to 2,000. The shape of the graph shows that as the sample size increases, sample error decreases. However, you should immediately notice that the graph is not a straight line. In other words, doubling sample size does not result in halving the sample error. The relationship is a curved one. It looks a bit like a ski jump lying on its back. There is another important property of the sample accuracy graph. As you look at the graph, note that at a sample size of around 500, the accuracy level drops below ±5% (it is actually ±4.4%), and it continues to decrease at a very slow rate with larger sample sizes. In other words, once a sample is greater than, say, 500, large gains in accuracy are not realized with large increases in the size of the sample. In fact, if it is already ±4.4% in accuracy, there is not much more accuracy possible. With the lower end of the sample size axis, however, large gains in accuracy can be made with a relatively small sample size increase. For example, with a sample size of 50, the accuracy level is ±13.9%, whereas with a sample size of 250, it is ±6.2%, meaning the accuracy of the 250 sample is roughly double that of the 50 sample. But as was just described, such huge gains in accuracy are not the case at the other end of the sample size scale because of the nature of the curved relationship. How to Calculate Sample Size The proper way to calculate sample size is to use the confidence interval formula for sample sizethat follows. ■ The confidence interval formula for sample size is the proper way to determine sample size. Sample size formula 􏰄 n z pq e = 2 2 ( ) Determining Size of a Sample 295 ■ Variability refers to how much respondents agree in their answer to a question. If everyone wanted the same thing on their pizza, there would be no variability. Where n =the calculated sample size z =standard error associated with the chosen level of confidence (typically, 1.96) p =estimated percentage in the population q =(100%−p) e =acceptable error (desired accuracy level) The confidence interval formula for sample size is based on three elements: variability, confidence level, and desired accuracy. We will describe each in turn. Variability: ptimesq This formula is used if we are focusing on some categorically scaled question in the survey. For instance, when conducting a Domino’s Pizza survey, our major concern might be the percentage of pizza buyers who intend to buy Domino’s. There are two possible answers: ―yes‖ or ―no.‖ If our pizza buyers population has very little variability, that is, if almost everyone, say, 90%, are raving Domino’s Pizza fans and shout ―Yes, yes, yes!‖ then this belief will be reflected in the sample size formula as 90% times 10%, or 900. However, if there is great variability, meaning that no two respondents agree and we have a 50%/50% split, ptimesqbecomes 50% times 50%, or 2,500, which is the largest possible ptimesqnumber possible. (There is a differ- ent formula for when you are trying to estimate an average. However, the percent- age formula is simpler and more commonly used, so we will restrict our coverage to the percentage formula.) The use of p=50%,q=50% is a research industry standard of sorts. As you can see, it is the most conservative p-qcombination, generating the largest sample size, so it is preferred when the researcher is uncertain or guessing about the variability. In fact, public opinion polling companies typically report the accuracy of their samples, and if you find such a report in a news article or other publication, and you reconstruct their calculation of their reported sample error, you will find that they have used 50/50. Alternatively, some researchers opt for a pilot study to deter- mine the approximate amount of variability.6 PRACTICAL APPLICATIONS 296 Chapter 10: Determining Sample Size and the Sampling Method Level of Confidence: z We need to decide on a level of confidence, and it is customary among marketing researchers to use the 95% level of confidence, in which the zis 1.96. If a researcher prefers to use the 99% level of confidence, the corresponding zis 2.58. We will describe how this level of confidence operates shortly. Desired Accuracy:e Lastly, the formula requires that we specify an acceptable level of sample error, meaning the ±% accuracy notion that we introduced to you. That is, the term eis the amount of sample error that will be associated with the survey. It is used to indi- cate how close your sample percentage finding will be to the true population per- centage if it were repeated many, many times. Figure10.2illustrates how the level of confidence figures into sample size accuracy. There is a theoretical notion that if the survey were repeated a great many times—several thousands of times—and if you plotted the frequency distribution of each pfor every one of these repeated samples, the pattern would appear as a bell curve, as you see in Figure10.2. Note that 95% of the replications would fall between the population p(50% in our example in Figure10.2) and ±e. Here is an example of a sample size calculation that you can follow to make certain that you understand how to use the sample size formula. Let us assume there is great expected variability (50%) and we want ±3% accuracy at the 95% level of confidence. ■ Desired accuracy of a sample is expressed as ein the sample size calculation formula. –Sample Error (Desired Accuracy) ±Sample Error (Desired Accuracy) +Sample Error (Desired Accuracy) 95% of the replications will fall between p = 50% Figure 10.2How Sample Error and the 95% Level of Confidence Theoretically Operate Sample size computed withp=50%,q=50%, ande=3%􏰄 n= × = = = 196 50 50 3 3842500 9 9600 9 1067 2 2 .() .(,) , , Determining Size of a Sample 297 Whenever you calculate the sample size, you are computing the number of respondents you should have participate fully in your survey. But invariably, sur- veys run into two difficulties that require an upward adjustment of the computed sample size. If you read Marketing Research Application10.1, you will learn about the two problems of ―incidence rate‖ and ―nonresponse‖ and how to adjust the sam- ple size to cope with these two problems. You will also find a list of other practical issues that often force researchers to make sample size adjustments. Adjusting Your Sample Size to Compensate for Incidence Rate, Nonresponse, and More Suppose that Scope mouthwash wanted to find out reactions to a new formula that provides for some whitening of the teeth and a degree of tartar control as well. The researcher and Scope managers come to agree on a sample size of 500, so the researcher purchases the names of 500 individuals from a sample supply company. The survey moves along, but the data collection company that is perform- ing the telephone interviews reports to the researcher that only 4 out of 5 people in the sample use mouthwash. In other words, the incidence rate, defined as the percent of individuals in the sample who qualify to take the survey, is 80%, meaning that 20%, or 100 names in the sample, are not usable. So, under this situation, the largest final sample size possible is 400. At the same time, the data collection company manager reports to the researcher that potential respondents who qualify are refusing to take the survey. This problem is referred to as nonresponse, or failures by qualified respondents to take part in the survey. The data collection company esti- mates a refusal rate of 40%, meaning that the response rate is 60%. A response rate of 60% means that only 60% of the 400 qualified respondents will be in the final sample. The researcher is now faced with a final sample size of 240, far smaller than the desired size of 500. To cope with the realities of incidence rate and nonre- sponse, researchers must make adjustments on their calcu- lated sample sizes. A simple adjustment formula is as follows. Adjusted Calculated (1/ (1/ sample =sample ×Incidence×Response size size rate%) rate %) Sample size adjustment formula 􏰄 If you apply this formula to our Scope mouthwash example, the computations are as follows. Adjusted Calculated (1/Incidence (1/Response sample size = sample size × rate) × rate) = 500 × (1/.8) ×(1/.6) = 500 × 1.25 ×1.67 = 1044 So, as can be seen here, incidence rates and nonresponse can combine to have a tremendous impact on the final sam- ple size of a survey, and astute marketing researchers will make estimates of the magnitudes of these problems and adjust the calculated sample size accordingly. There are other factors that may force sample size adjust- ments. Susie Sangren, President, Clearview Data Strategy, has contributed the following list of practical constraints that researchers are likely to encounter: ■ Time pressure. Often research results are needed ―yesterday,‖ meaning that the sample size may be reduced to save time. ■ Cost constraint. A limited amount of money is available for the study, and limited funds translate to reduced sample size. ■ Study objective. What is the purpose of the study? A decision that does not need great precision can make do with a very small sample size such as a few focus groups or a pilot study. ■ Data analysis procedures. Some advanced data-analysis procedures require much-larger-than-ordinary sample sizes in order to be fully utilized.a a Personal communication to author from Susie Sangren. Sample size adjustment example 􏰅 MARKETING RESEARCH APPLICATION 10.1 298 Chapter 10: Determining Sample Size and the Sampling Method . Figure 10.3XL Data Analyst Setup for Sample Size Calculation USING THE XL DATA ANALYST TO CALCULATE SAMPLE SIZE It is time for you to be introduced to the XL Data Analyst Excel macro software that accompanies this textbook. There is a more formal introduction in the following chapter, the first data analysis chapter in this textbook. The XL Data Analyst is primarily a set of data analysis procedures that are easy to use and interpret. But there is a computational aid included in the XL Data Analyst that pertains to sam- ple size. For now, all you need to do is open up any Excel file that accompanies this textbook. Because the XL Data Analyst isan Excel macro, you will need to set the Excel 2003 version security at Medium or Low (Tools—Macros—Security— checkMediumorLow). Then click on ―Enable Macros‖ when the XL Data Analyst file loads into Excel. With Excel 2007, enable the macro content via the Security Warning feature after the file is loaded. After the file is loaded, you will see a ―Data‖ worksheet and a ―Define Variables‖ worksheet, but you can ignore whatever you see on these worksheets. Instead, use the XL Data Analyst to access the ―Calculate‖ function available in its main menu. The XL DataAnalyst will calculate sample size using the confidence sample size formula we have described in this chapter. As you can see in Figure10.3, we have ―pinned‖ the XL Data Analyst menu item on the Excel 2007 Quick Access tool bar, and the menu sequence is Calculate—Sample Size, which opens up the selection window where you can specify the allowable error (desired sample accuracy) and the estimated percent, p, value. In our example, we have set the accuracy level at 4% and the estimated pat 60%. Figure10.4reveals that the XL Data Analyst has computed the sample size for the 95% level of confidence to be 576, while for the 99% confidence level, the ■ The XL Data Analyst performs sample size calculations and provides sensitivity analysis for variability and sample error. XLDA Determining Size of a Sample 299 Figure 10.4XL Data Analyst Sample Size Calculation Output calculated sample size is 998. There are two tables following the Sample Size Table that a researcher can use to inspect the sensitivity of the sample size to slight variations of e(with estimated pconstant), ranging in our example from 3.0% to 5.0% by .5% increments, or variations in the estimated p(withecon- stant), ranging from 50% to 70% by 5% increments. The sensitivity analysis tables are provided so a researcher who is wrestling with a sample size decision can quickly compare the impact of small differences in his or her assumptions about variability in the population (p) as well as slightly loosening or tightening the sample accuracy requirements, or allowable error. Marketing managers and other clients of marketing researchers do not have a thorough understanding of sample size. In fact, they tend to have a belief in a false ―law of large sample size.‖ That is, they often confuse the size of the sample with the representativeness of the sample. As you will soon learn in reading about sam- ple selection procedures, the way the sample is selected, not its size, determines its representativeness. Also, as you have just learned, the accuracy benefits of exces- sively large samples are typically not justified by their increased costs. It is an ethical marketing researcher’s responsibility to try to educate a client on the wastefulness of excessively large samples. Occasionally, there are good reasons for having a very large sample, but whenever the sample size exceeds that of a typ- ical national opinion poll (1,200 respondents), justification is required. Otherwise, the manager’s cost will be unnecessarily inflated. Unethical researchers may recom- mend very large samples as a way to increase their profits, which may be set at a percentage of the total cost of the survey. They may even have ownership in the data collection company slated to gather the data at a set cost per respondent. It is important, therefore, that marketing managers know the motivations underlying the sample size recommendations of the researchers they hire. 290 - 299). <vbk:#page(290)> HOW TO SELECT A REPRESENTATIVE SAMPLE You now know that surprisingly few individuals can be chosen in a sample that rep- resents a population with a small amount of sample error. We now turn to the selec- tion process, for if the sample selection method is faulty or biased, our findings will be compromised. For example, if Starbucks Coffee wanted to find out how its cus- tomers feel about Starbucks coffee and other food products and it used a sample of customers drawn from those who happened to make a purchase at its Miami International Airport location on June 12, this sample would not be truly represen- tative of all Starbucks Coffee customers. It would only represent Starbucks Coffee customers of that location in that time period. Probability Sampling Methods Arandom sampleis one in which every member of the population has an equal chance, or probability, of being selected into that sample. Sample methods that embody random sampling are often termed probability sampling methods, because the chance of selection can be expressed as a probability. We will describe four probability sampling methods: simple random sampling, systematic sampling, clus- ter sampling, and stratified sampling. You can use Table10.1as a handy reference, for it summarizes the basics of each of these sampling techniques. How to Select a Representative Sample 301 Simple random sampling is like a lottery because everyone has an equal chance of being selected. ■ Simple random sampling makes use of random numbers to select each individual into the sample. Simple Random Sampling With simple random sampling, the probability of being selected into the sample is ―known‖ and equal for all members of the population. This sampling technique is expressed by the following formula: 􏰆Formula for sample selection probability Probability of selection =sample size/population size So, with simple random sampling, if the researcher was surveying a population of 100,000 recent DVD player buyers with a sample size of 1,000 respondents, the probability of selection on any single population member into this sample would be 1,000 divided by 100,000, or 1 out of 100, calculated to be 1%. There are some vari- ations of simple random sampling, but the table of random numbers technique best exemplifies simple random sampling. Therandom numbers techniqueis an application of simple random sampling that uses the concept of a table of random numbers, which is a listing of numbers whose nonsystematic (or random) order is assured. Before computer-generated random numbers were widespread, researchers used physical tables that had num- bers with no discernible relationship to each other. If you looked at a table of random numbers, you would not be able to see any systematic sequence of the numbers regardless of where on the table you began and whether you went up, down, left, right, or diagonally across the entries. USING THE XL DATA ANALYST TO GENERATE RANDOM NUMBERS You can use the XL Data Analyst to generate your own table of ran- dom numbers. Figure10.5shows the menu command sequence and setup window to accomplish this end. Note that the menu sequence is ―Calculate—Random #’s,‖ and the selection window allows you to specify how many random integer numbers you want (up to 9,999), XLDA 302 Chapter 10: Determining Sample Size and the Sampling Method . Figure 10.5XL Data Analyst Setup for Random Numbers and you can also specify the largest possible value (up to 999,999,999). In our example, we have specified 100 random numbers with a maximum value of 1,000. Figure10.6displays our random numbers. Notice that they are arranged in five columns. You can experiment with the random-number-table-generator function of the XL Data Analyst, and you should discover that there is no sys- tematic pattern relating these numbers to one another. Figure 10.6XL Data Analyst Output for Random Numbers How to Select a Representative Sample 303 ■ With a random numbers technique, you must have unique number values assigned to all members of the population. ■ Random digit dialing and the ―plus-one‖ dialing technique incorporate the simple random sampling method. With the random numbers technique, you must have unique number values assigned to each of the members of your population. You might use social security numbers because these are unique to each person, or you may have the computer, such as in a database program, assign unique numbers to them, and do the matching work to determine what individuals are selected into the sample. Again, the use of random numbers assures the researcher that every population member who is present in the master list or file will have an equal chance of being selected into the sample. If a researcher is using telephone numbers and drawing a sample, this technique is referred to as random digit dialing. This approach is used in telephone surveys to overcome the problems of unlisted and new telephone numbers. Unlisted numbers are a growing concern not only for researchers in the United States but in all industrialized countries such as those in Europe as well.7In random digit dialing, telephone numbers are generated randomly with the aid of a computer. Telephone interviewers call these numbers and administer the survey to the respondent once the person has been qualified. However, random digit dialing may result in a large number of calls to nonexisting telephone numbers. A popular variation of random digit dialing that reduces this problem is the plus-one dialing procedure, in which numbers are selected from a telephone directory, and a digit, such as a ―1,‖ is added to each number to determine which telephone number is then dialed. Systematic Sampling Before widespread use of computerized databases, researchers used hard-copy lists. In this situation, systematic samplingis a way to select a simple random sample from a directory or list that is much more efficient (uses less effort) than with simple ran- dom sampling, because with a physical list, the researcher must scan all the names to match up each random number. To apply the systematic sampling technique in the special case of a physical listing of the population, such as a membership directory or a telephone book, systematic sampling can be applied with less difficulty and accom- plished in a shorter time period than can simple random sampling. Furthermore, in many instances, systematic sampling has the potential to create a sample that is almost identical in quality to samples created from simple random sampling. To use systematic sampling, it is necessary to obtain a hard-copy listing of the population, but it is not necessary to have a unique identification number assigned to each member on the list. The goal of systematic sampling is to literally ―skip‖ through the list in a systematic way, but to begin at a random starting point in the list. That is, the research calculates a ―skip interval‖ using the following formula: 􏰆Formula for skip interval Skip interval =population list size/sample size For example, if the skip interval is calculated to be 100, the researcher will select every 100th name in the list. This technique is much more efficient than searching for matches to random numbers. The use of this skip interval formula ensures that the entire list will be covered. The random sample requirement is implemented by the use of a random starting point, meaning that the researcher must use some random number technique to decide on the first name in the sam- ple. Subsequent names are selected by using the skip interval. Because a random starting point is used, every name on the list has an equal probability of being selected into the systematic sample. If you are drawing a systematic sample from a 304 Chapter 10: Determining Sample Size and the Sampling Method ■ Systematic sampling is more efficient than simple random sampling, and it ensures random selection of the sample. directory of thousands of names, it would be daunting to count to, say, the 44,563rd name, so after pondering a bit, you might realize that you could draw a single random number from 1 to the number of pages in the directory to randomly select a page, then draw a random number from 1 to the number of columns on the page to select the random column, and finally, select a random number between 1 and the number of names in that column. Thus, three quickly drawn random num- bers would effect the random starting point for your systematic sample. Cluster Sampling Another form of probability sampling is known as cluster sampling, in which the population is divided into subgroups, called ―clusters,‖ each of which represents the entire population.8Note that the basic concept behind cluster sampling is very similar to the one described for systematic sampling, but the implementation dif- fers. The procedure identifies identical clusters. Any one cluster, therefore, will be a satisfactory representation of the population. Cluster sampling is advantageous when there is no electronic database of the population. It is easy to administer, and cluster sampling goes a step further in striving to gain economic efficiency over simple random sampling by simplifying the sampling procedure used. We illustrate cluster sampling by describing a type of cluster sample that is sometimes referred to as ―area sampling.‖ Inarea sampling, the researcher subdivides the population to be surveyed into geographic areas, such as census tracts, cities, neighborhoods, or any other conve- nient and identifiable geographic designation. The researcher has two options at this point: a one-step approach or a two-step approach. In the one-step area sample approach, the researcher may believe the various geographic areas to be sufficiently identical to permit him or her to concentrate his or her attention on just one area and then generalize the results to the full population. But the researcher would need to select that one area randomly and perform a census of its members. Alternatively, he or she may employ a two-step area sampleapproach to the sampling process. That is, for the first step, the researcher could select a random sample of areas, and then for the second step, he or she could decide on a probability method to sample individuals within the chosen areas. The two-step area sample approach is preferable to the one-step approach because there is always the possibility that a single cluster may be less representative than the researcher believes. But the two- step method is more costly because more areas and time are involved.9 Stratified Sampling All of the sampling methods we have described thus far implicitly assume that the population has a normal or bell-shaped distribution for its key properties. That is, there is the assumption that every potential sample unit is a fairly good representa- tion of the population, and any who are extreme in one way are perfectly counter- balanced by opposite extreme potential sample units. Unfortunately, in marketing research it is common to work with populations that contain unique subgroupings; you might encounter a population that is not distributed symmetrically across a normal curve. With this situation, unless you make adjustments in your sample design, you will end up with a sample that is inaccurate. One solution is stratified sampling, which separates the population into different subgroups and then samples all of these subgroups using a random sampling technique. ■ Area sampling is a practical application of cluster sampling in which geographic areas are used to represent the clusters. How to Select a Representative Sample 305 1 Not at all To what extent do you value a college degree? Key: F Freshmen S Sophomores Jr Juniors Sr Seniors = = = = 2 F S Jr Sr Freshmen mean 345 Very highly Sophomores mean Juniors mean Seniors mean Figure 10.7Illustration of Four Strata in a Stratified Population of Undergraduate University Students For example, let’s take the case of a college that is attempting to assess how its students perceive the quality of its educational programs. A researcher has formu- lated the question ―To what extent do you value your college degree?‖ The response options are along a 5-point scale, where 1 equals ―not valued at all‖ and 5 equals ―very highly valued.‖ The population of students is defined by year: freshman, sophomore, junior, and senior. It seems reasonable to believe that the averages will differ by the respondent’s year status because seniors probably value a degree more than do juniors, who value a degree more than do sophomores, and so on. At the same time, it is expected that seniors would be more in agreement (have less vari- ability) than would underclass-persons. This belief is due to the fact that freshmen are students who are trying out college, some of whom are not serious about com- pleting it and do not value it highly, but some of whom are intending to become doctors, lawyers, or professionals whose training will include graduate degree work as well as their present college work. The serious freshmen students would value a college degree highly, whereas the less serious ones would not, meaning that we would find much variability in the freshmen students, less variability in sopho- mores, still less in juniors, and the least with college seniors. The situation might be something similar to the distributions illustrated in Figure10.7. When you look at Figure10.7, you will find that the average score for each class is successively higher, with freshmen at the lowest average and seniors at the highest average. Also, the bell-shaped curve for each group, or stratum, is suc- cessively narrower, meaning that there is great variability in the freshman stratum, but much less in the senior stratum of our population. What would happen if we used a simple random sample of equal size for each of our college groups? Because sample accuracy is determined by the variability in the population—regardless of whether you assess variability by using ptimesqfor categorical questions or by using the standard deviation for metric scales—in our student example, we would be least accurate with freshmen and most accurate with ■ With stratified sampling, the population is separated into different strata and a sample is taken from each stratum. 306 Chapter 10: Determining Sample Size and the Sampling Method With stratified sampling, the researcher identifies subgroups or strata in the population and samples each stratum. seniors. To state this situation differently, we would be statistically overefficient with seniors and statistically underefficient with freshmen because we would be oversampling the seniors and undersampling the freshmen. To gain overall statisti- cal efficiency, we should draw a larger sample of freshmen and a smaller one of seniors. We might do this by allocating the sample proportionately based on the total number of the freshmen, sophomores, juniors, and seniors, each taken as a percentage of the whole college population. (Normally, there are fewer seniors than juniors than sophomores than freshmen in a college.) Thus, we would be drawing the smallest sample from the seniors group, who have the least variability in their assessments of the value of their college education, and the largest sample from the freshmen, who have the most variability in their assessments. We established in our sample size calculation section that smaller sample sizes will occur for highly simi- lar populations (e.g, 90% times 10%), while large sample sizes will be calculated for highly dissimilar populations (e.g., 50% times 50%). With stratified sampling, the researcher takes a skewed populationand identifies the subgroups or stratacontained within it based on their differences. In other words, each stratum is different from the other strata that make up the entire pop- ulation. Then simple random sampling, systematic sampling, or some other type of probability sampling procedure is applied to draw a sample from each stratum. The stratum sample sizes can differ based on knowledge of the variability in each popu- lation stratum and with the aim of achieving the greatest overall sample accuracy. How does stratified sampling result in a more accurate overall sample? There are two ways this accuracy is achieved. First, stratified sampling allows for explicit analysis of each stratum. The college degree example illustrates why a researcher would want to know about the distinguishing differences between the strata in order to assess the true picture. Each stratum represents a different response pro- file, and by allocating sample size based on the variability in the strata profiles, a more efficient sample design is achieved. Second, there is a procedure that allows the estimation of the overall popula- tion average by use of a weighted averagefor a stratified sample, whose formula takes into consideration the sizes of the strata relative to the total population size and applies those proportions to the strata’s averages. The population average is cal- culated by multiplying each stratum by its proportion and summing the weighted ■ Stratified sampling separates the population into dissimilar groups, called strata, because the researcher is working with a skewed population. How to Select a Representative Sample 307 stratum averages. This formula results in an estimate that is consistent with the true distribution of the population when the sample sizes used in the strata are not proportionate to their shares of the population. Here is the formula that is used for two strata: ■ Use a weighted average formula when combining strata averages taken in stratified sampling. 􏰆Formula for weighted average Average population=(averageA)(proportionA)+(averageB)(proportionB) where A signifies stratum A, and B signifies stratum B. Here is an example. A researcher separated a population of households that rent videos on a regular basis into two strata. Stratum A was families without young children and stratum B was families with young children. When asked to use a scale of 1=―poor‖ and 5=―excellent‖ to rate their video rental store on its video selection, the means were computed to be 2.0 and 4.0, respectively, for the samples. The researcher knew from census information that families without young children accounted for 70% of the population, whereas families with young children accounted for the remaining 30%. The weighted mean rating for video selection was then computed as (.7)(2.0)+(.3)(4.0)=2.6. Usually, a surrogate measure, which is some observable or easily determined characteristic of each population member, is used to help partition or separate the population members into their various subgroupings. For example, in the instance of the college, the year classification of each student is a handy surro- gate. With its internal records, the college could easily identify students in each stratum, and this determination would be the stratification method. Of course, there is the opportunity for the researcher to divide the population into as many relevant strata as necessary to capture different subpopulations. For instance, the college might want to further stratify on college of study, gender, or grade point average (GPA) ranges. Perhaps professional-school students value their degrees more than do liberal arts students, females differently from male students, and high-GPA students more than average-GPA or failing students. The key issue is that the researcher should use some basis for dividing the population into strata that results in different responses across strata. There is no need to stratify if all strata respond alike. If the strata sample sizes are faithful to their relative sizes in the population, you have what is called a proportionate stratified sampledesign. Here you do not use the weighted formula, because each stratum’s weight is automatically accounted for by its sample size. But with disproportionate stratified sampling, the weighted for- mula needs to be used, because the strata sizes do not reflect their relative propor- tions in the population. Nonprobability Sampling Methods The four sampling methods we have described thus far embody probability sam- pling assumptions. In each case, the probability of any unit being selected from the population into the sample is known, and it can be calculated precisely given the sample size, population size, and strata or cluster sizes, if they are used. With a nonprobability sampling method, selection is not based on fairness, equity, or equal chance. One author has noted that nonprobability sampling uses human interven- tion, while probability sampling does not.10In fact, a nonprobability sampling 308 Chapter 10: Determining Sample Size and the Sampling Method Table10.2 Four Different Nonprobability Sampling Techniques Convenience Sampling The researcher uses a high-traffic location such as a busy pedestrian area or a shopping mall to intercept potential respondents. Sample selection error occurs in the form of the absence of members of the population who are infrequent or nonusers of that location. Judgment Sampling The researcher uses his or her judgment or that of some other knowledgeable person to identify who will be in the sample. Subjectivity enters in here, and certain members of the population will have a smaller chance of selection into the sample than will others. Referral Sampling Respondents are asked for the names or identities of others like themselves who might qualify to take part in the survey. Members of the population who are less well known, disliked, or whose opinions conflict with the respondent have a low probability of being selected into a referral sample. Quota Sampling The researcher identifies quota characteristics such as demographic or product-use factors and uses these to set up quotas for each class of respondent. The sizes of the quotas are determined by the researcher’s belief about the relative size of each class of respondent in the population. Often quota sampling is used as a means of ensuring that convenience samples will have the desired proportions of different respondent classes, thereby reducing the sample selection error but not eliminating it. ■ Nonprobability samples do not embody fairness, equity, or equal chance. method is inherently biased, and the researcher acknowledges that the sample is representative only to some degree that the researcher feels is sufficient under the circumstances of the survey. To be candid about it, most nonprobability sampling methods take shortcuts that save effort, time, and money, but which obliterate the equal-chance guarantee of any probability sampling method. As a result, you can- not in good conscience calculate the probability of any one person in the popula- tion being selected into a nonprobability sample. So, why in the world would a researcher ever want to use a nonprobability sam- ple? There are three answers to this question, and we just divulged them—effort, time, and money. Compared to random sampling techniques, nonrandom ones, meaning nonprobability sampling methods, take less effort, they are faster, and they cost less. But these savings have a cost that ethical researchers readily acknowledge, and that cost is diminished representativeness. Nonetheless, it is important that you become familiar with nonprobability sampling methods as there are instances, such as when conducting a pretest or a pilot study, when a nonrandom sampling technique is useful. Alternatively, you should be able to identify when a nonran- dom sample has been utilized, so that you can make your own informed judgment as to the representativeness of the sample. There are four nonprobability sampling methods: convenience samples, judg- ment samples, referral samples, and quota samples. A discussion of each method follows, and you can refer to Table10.2, which summarizes how each of these non- probability sampling techniques operate. How to Select a Representative Sample 309 Convenience Samples Aconvenience sampleis a sample drawn at the convenience of the researcher or inter- viewer. Accordingly, the most convenient areas to a researcher in terms of time and effort turn out to be high-traffic areas such as shopping malls, or busy pedestrian intersections. The selection of the place and, consequently, prospective respondents is subjective rather than objective. Certain members of the population are automati- cally eliminated from the sampling process.11For instance, there are those people who may be infrequent or even nonvisitors of the particular high-traffic area being used. On the other hand, in the absence of strict selection procedures, there are mem- bers of the population who may be omitted because of their physical appearance, general demeanor, or by the fact that they are in a group rather than alone. One author states, ―Convenience samples ... can be seriously misleading.‖12 Mall-intercept companies often use a convenience sampling method to recruit respondents. For example, shoppers are encountered at large shopping malls and quickly qualified with screening questions. For those satisfying the desired popula- tion characteristics, a questionnaire may be administered or a taste test performed. Alternatively, the respondent may be given a test product and asked if he or she would use it at home. A follow-up telephone call some days later solicits his or her reaction to the product’s performance. In this case, the convenience extends beyond easy access of respondents into considerations of setup for taste tests, storage of prod- ucts to be distributed, and control of the interviewer workforce. Additionally, large numbers of respondents can be recruited in a matter of days. The screening questions and geographic dispersion of malls may appear to reduce the subjectivity inherent in the sample design, but in fact the vast majority of the population was not there and could not be approached to take part. Yet, there are ways of controlling convenience sample selection error using a quota system, which we discuss shortly. Judgment Samples Ajudgment sampleis somewhat different from a convenience sample in concept because a judgment sample requires a judgment or an ―educated guess‖ as to who should represent the population. Often the researcher or some individual helping the ■ A convenience sample relies on high-traffic areas where some members of the target population pass by. With a convenience sample, the researcher selects high- traffic locations and interviews individuals who happen to be there. 310 Chapter 10: Determining Sample Size and the Sampling Method ■ Judgment samples rely on someone specifying what individuals are typical or judged to be representative of the population in some way. researcher who has considerable knowledge about the population will choose those individuals that he or she feels constitute the sample. It should be apparent that judg- ment samples are highly subjective and therefore prone to much error. However, judgment samples do have special uses. For instance, in the prelimi- nary stages of a research project, the researcher may use qualitative techniques such as depth interviews or focus groups as a means of gaining insight and understanding to the research problem. In this case, judgment sampling is a quick, inexpensive, and acceptable technique because the researcher is not seeking to generalize the findings of this sample to the population as a whole. Take, for example, a recent focus group concerning the need for a low-calorie, low-fat microwave oven cook- book. Twelve women were selected as representative of the present and prospective market. Six of these women had owned a microwave oven for 10 or more years, 3 of the women had owned the oven for less than 10 years, and 3 of the women were in the market for a microwave oven. In the judgment of the researcher, these 12 women represented the population adequately for the purposes of the focus group. It must be quickly pointed out, however, that the intent of this focus group was far different from the intent of a survey. Consequently, the use of a judgment sample was consid- ered satisfactory for this particular phase in the research process for the cookbook. The focus group findings served as the foundation for a large-scale regional survey conducted two months later that relied on a probability sampling method. Referral Samples Areferral sampleis sometimes called a ―snowball sample,‖ because it requires respondents to provide the names of additional respondents. Such lists begin when the researcher compiles a short list of potential respondents based on convenience or judgment. After each respondent is interviewed, he or she is queried about the names of other possible respondents. In this manner, additional respondents are referred by previous respondents. Or, as the other name implies, the sample grows just as a snowball grows when it is rolled downhill. Referral samples are most appropriate when there is a limited and disappointingly short sample frame and when respondents can provide the names of others who would qualify for the survey. For example, some foreign countries have low telephone penetration or slow mail systems that make these options unsuitable, while a referral approach adds an element of trust to the approach for each new potential respondent. The nonprobability aspects of referral sampling come from the selectivity used throughout. The initial list may also be special in some way, and the primary means of adding people to the sample is by tapping the memories of those on the original list. Referral samples are often useful in industrial marketing research situations.13 Quota Samples We have saved the most commonly used nonprobability sampling method for last. Thequota sampleestablishes a specific quota for various types of individuals to be interviewed. The quotas are determined through application of the research objec- tives and are defined by key characteristics used to identify the population. In the application of quota sampling, a fieldworker is provided with screening criteria that will classify the potential respondent into a particular quota cell. For example, if the interviewer is assigned to obtain a sample quota of 50 each for black females, black males, white females, and white males, the qualifying characteristics would be race and gender. Assuming our fieldworkers were conducting mall intercepts, 300 - 310). <vbk:#page(300)> ■ Referral samples make use of respondents’ volunteering names of friends and others whose names they know 310). <vbk:#page(310)> each would determine through visual inspection which category the prospective respondent fits into, and would work toward filling the quota in each of the four cells. So a quota system overcomes much of the nonrepresentativeness danger inherent in convenience samples.14 The popularity of quota samples is attributable to the fact that they combine non- probability sampling advantages with quota controls that ensure the final sample will approximate the population with respect to its key characteristics. Quota samples are often used by consumer goods companies that have a firm grasp on the features char- acterizing the individuals they wish to study in a particular marketing research proj- ect. These companies often use mall-intercept data collection companies that deliver fast service at a reasonable price, and the use of quota controls guarantees that the final sample will satisfactorily represent the population that the consumer goods company has targeted for the research project. Quota samples are also used in global marketing research where communication systems are problematic. For example, most companies performing research in Latin America use quota samples.15When done conscientiously and with a firm understanding of the quota characteristics, quota sampling can rival probability sampling in the minds of some researchers. ONLINE SAMPLING TECHNIQUES As you know, Internet surveys are becoming popular. To be sure, sampling for Internet surveys poses special challenges,16but most of these issues can be addressed in the context of our probability and nonprobability sampling concepts.17If you understand how a particular online sampling method works, you can probably interpret the sam- pling procedure correctly with respect to basic sampling concepts.18For purposes of illustration, we will describe three types of online sampling: (1)random online inter- cept sampling, (2)invitation online sampling, and (3)online panel sampling. Random online intercept samplingrelies on a random selection of Web site visi- tors. There are a number of Java-based or other html-embedded routines that will select Web site visitors on a random basis such as time of day or random selection from the stream of Web site visitors. If the population is defined as Web site visi- tors, then this is a simple random sample of these visitors within the time frame of the survey. If the sample selection program starts randomly and incorporates a skip interval system, it is a systematic sample,19and if the sample program treats the population of Web site visitors like strata, it uses stratified simple random sampling as long as random selection procedures are used faithfully. However, if the popula- tion is other than Web site visitors, and the Web site is used because there are many visitors, the sample is akin to a mall-intercept sample (convenience sample). Invitation online samplingis when potential respondents are alerted that they may fill out a questionnaire that is hosted at a specific Web site.20For example, a retail store chain may have a notice that is handed to customers with their receipts notifying them that they may go online to fill out the questionnaire. However, to avoid spam, online researchers must have an established relationship with potential respondents who expect to receive an e-mail survey. If the retail store uses a ran- dom sampling approach such as systematic sampling, a probability sample will result. Similarly, if the e-mail list is a truly representative group of the population, and the procedures embody random selection, it will constitute a probability sample. However, if in either case there is some aspect of the selection procedure ■ Online sampling can be interpreted in the context of traditional sampling techniques. ONLINE 312 Chapter 10: Determining Sample Size and the Sampling Method that eliminates population members or otherwise overrepresents elements of the population, the sample will be a nonprobability one. Online panel samplingrefers to consumer or other respondent panels that are set up by marketing research companies for the explicit purpose of conducting online surveys with representative samples. There is a growing number of these compa- nies, and online panels afford fast, convenient, and flexible access to preprofiled samples.21Typically, the panel company has several thousand individuals who are representative of a large geographic area, and the market researcher can specify sample parameters such as specific geographic representation, income, education, family characteristics, and so forth. The panel company then uses its database on its panel members to broadcast an e-mail notification to those panelists who qualify according to the sample parameters specified by the market researcher. Although online panel samples are not probability samples, they are used extensively by the marketing research industry.22In some instances, the online panel company creates the questionnaire; at other times, the researcher composes the questionnaire on the panel company’s software, or some other means of questionnaire design might be used, depending on the services of the panel company. One of the greatest pluses of online panels is the high response rate, which ensures that the final sample closely represents the population targeted by the researcher. Other online sampling approaches are feasible and limited only by the creativity of the sample designers. SUMMARY This chapter dealt with the sample aspects of a marketing research survey. We began by defining basic terms such as sample, population, census, sampling error, sample frame, and sample frame error. We then described the notions associated with the confidence interval method of calculating sample size. The formula for this method requires that the researcher (1)specify a sample accuracy level such as ±3% or ±4%; (2)estimate the variability in the population, which can be taken to be 50%/50% if the researcher is unsure; and (3)use the 95% or 99% level of confi- dence. You can calculate sample size with the formula or use the XL Data Analyst. The chapter then took up sample selection methods, and it described four probability sampling methods, which are techniques that guarantee that each mem- ber of the population has an equal chance of being selected into the sample. These four techniques were: (1)simple random sampling where random numbers are employed; (2)systematic sampling that utilizes a skip interval for a sample frame list; (3)cluster sampling if the researcher can identify homogeneous groups in the population; and (4)stratified sampling, used for skewed populations. Next, four nonprobability sample methods were described, and it was pointed out for each one how its application incurs some degree of sample selection error. These tech- niques were (1)convenience sampling such as using a shopping mall’s customer traffic as the sample frame; (2)judgment sampling, where someone arbitrarily specifies who will be in the sample; (3)referral sampling, in which case the respon- dents divulge the names of friends and acquaintances to the researcher; and (4)quota sampling, where the researcher attempts to minimize sample selection error by requiring that certain classes of individuals are in the sample in propor- tions that are believed to reflect their presence in the population. Review Questions 313 KEY TERMS Population(p.292) Sample(p.292) Census(p.292) Sampling error(p.292) Sample frame(p.292) Sample frame error(p.293) Accuracy of a sample(p.293) Confidence interval formula for sample size(p.294) Variability(p.295) Level of confidence(p.296) Desired accuracy(p.296) Incidence rate(p.297) Nonresponse(p.297) Random sample(p.300) Probability sampling methods(p.300) Simple random sampling(p.301) Random numbers technique(p.301) Table of random numbers(p.301) Random digit dialing(p.303) Plus-one dialing procedure(p.303) Systematic sampling(p.303) ―Skip interval‖(p.303) Random starting point(p.303) Cluster sampling(p.304) Area sampling(p.304) One-step area sample(p.304) Two-step area sample(p.304) Stratified sampling(p.304) Skewed population(p.306) Strata(p.306) Weighted average(p.306) Surrogate measure(p.307) Proportionate stratified sample(p.307) Disproportionate stratified sampling (p.307) Nonprobability sampling method (p.307) Convenience sample(p.309) Judgment sample(p.309) Referral sample(p.310) Quota sample(p.310) Random online intercept sampling (p.311) Invitation online sampling(p.311) Online panel sampling(p.312) REVI EW QUESTI ONS 1 Define each of the following: a Population bSample c Census dSample frame 2 Indicate the sample frame error typically found in the households listing of a telephone book. 3 Explain what is meant by the accuracy of a sample. 4 Why is ptaken to represent the variability of a population? 5 Why is a probability sample also a random sample? 7 How are random numbers vital to a probability sample method? 8 How is sample frame error overcome with a ―plus-one‖ dialing procedure? 9 What single step is critical in preserving the probability characteristic of a sys- tematic sample? Why? 10 How does cluster sampling differ from stratified sampling? 11 When is a weighted mean required for a stratified sample? Explain when and why it is not required. 12 What is convenient about a convenience sample? 13 Compare a judgment sample to a referral sample. How are they similar? How are they unalike? 314 Chapter 10: Determining Sample Size and the Sampling Method 14 In order to implement a quota sample, what prior knowledge does the researcher need to have about the population? APPLI CATI ON QUESTI ONS 15 Here are four populations and a potential sample frame for each one. With each pair, identify: (1)members of the population who are not in the sample frame, and (2)sample frame items that are not part of the population. Also, for each one, would you judge the amount of sample frame error to be acceptable or unacceptable? Population Sample Frame a. Buyers of Scope mouthwash Mailing list of Consumer Reportssubscribers b. Listeners of a particular FM radio classical music station Telephone directory in your city Members of Sales and Marketing Executives International (a national organization of sales managers) c. Prospective buyers of a new day planner and prospective-client tracking kit d. Users of weatherproof decking materials (to build outdoor decks) Individuals’ names registered at a recent home and garden show 16 Here are some numbers that you can use to sharpen your computational skills for sample size determination. Crest toothpaste is reviewing plans for its annual sur- vey of toothpaste purchasers. With each case that follows, calculate the sample size pertaining to the key variable under consideration. Where information is missing, provide reasonable assumptions. You can check your computations by using the sample size calculation feature of the XL Data Analyst. Acceptable Confidence Case Key Variable Variability Error Level 1 Market share of Crest 23% share 4% 95% toothpaste last year 2 Percentage of people who Unknown 5% 99% brush their teeth per week 3 How likely Crest buyers 30% switched 5% 95% are to switch brands last year 4 Percentage of people who 20% two years 3.5% 95% want tartar-control ago; 40% one features in their toothpaste year ago 5 Willingness of people Unknown 6% 99% to adopt the toothpaste Application Questions 315 17 Allbookstores.com has a used-textbook division. It buys its books in bulk from used-book buyers who set up kiosks on college campuses during final exams, and it sells the used textbooks to students who log on to the Allbookstores.com Web site via a secured credit card transaction. The used texts are then sent by United Parcel Service to the student. The company has conducted a survey of used-book buying by college stu- dents each year for the past four years. In each survey, 1,000 randomly selected college students have been asked to indicate whether or not they bought a used textbook in the previous year. The results are as follows: Years Ago 1234 Percentage buying used text(s) 70% 60% 55% 50% What are the sample size implications of these data? That is, assess whether or not the survey should be continued in the coming year with a sample size of 1,000. 18 Pet Insurers Company markets health and death benefits insurance to pet owners. It specializes in coverage for pedigreed dogs, cats, and expensive and exotic pets such as miniature Vietnamese potbellied pigs. The veterinary care costs of these pets can be high, and their deaths represent substantial financial loss to their own- ers. A researcher working for Pet Insurers finds that a listing company can provide a list of 15,000 names that includes all current subscribers to Cat Lovers,Pedigreed Dog, and Exotic Pets Monthly. If the final sample size is to be 1,000, calculate what the skip interval should be in a systematic sample for each of the following: a a telephone survey using drop-down replacement of nonrespondents b a mail survey with an anticipated 30% response rate (assume the incidence rate for this sample frame to be 100%) 19 A market researcher is proposing a survey for the Big Tree Country Club, a pri- vate country club that is contemplating several changes in its layout to make the golf course more championship caliber. The researcher is considering three different sample designs as a way to draw a representative sample of the club’s golfers. The three alternative designs are: a Station an interviewer at the first-hole tee on one day chosen at random, with instructions to ask every 10th golfer to fill out a self-administered questionnaire. b Put a stack of questionnaires on the counter where golfers check in and pay for their golf carts. There would be a sign above the questionnaires, and there would be an incentive for a ―free dinner in the clubhouse‖ for three players who fill out the questionnaires and whose names are selected by a lottery. c Using the city telephone directory, a plus-one dialing procedure would be used. With this procedure a random page in the directory would be selected, and a name on that page would be selected, both using a table of random numbers. The plus-one system would be applied to that name and every name listed after it until 1,000 golfers are identified and interviewed by telephone. Assess the representativeness and other issues associated with this sample problem. Be sure to identify the sample method being contemplated in each case. Which sample method do you recommend using and why? 316 Chapter 10: Determining Sample Size and the Sampling Method I NTERACTI VE LEARNI NG You can visit the textbook Web site at www.prenhall.com/burnsbush. Use the self-study quizzes and get instant feedback on whether or not you need additional studying to master the material in this chap- ter. You can also review the chapter’s major points by visiting the chapter outline and key terms. CASE 10.1 Peaceful Valley: Trouble in Suburbia Located on the outskirts of a large city, the suburb of Peaceful Valley comprises approximately 6,000 upscale homes. The subdivision came about 10 years ago when a developer built an earthen dam on Peaceful River and created Peaceful Lake, a meandering 20-acre body of water. The lake became the centerpiece of the develop- ment, and the first 2,000 one-half-acre lots were sold as lakefront property. Now Peaceful Valley is fully devel- oped, with 50 streets, all approximately 1.5 miles in length, with approximately 60 houses on each street. Peaceful Valley’s residents are primarily young, profes- sional, dual-income families with one or two school-age children. A unique feature of Peaceful Valley is that there are only two entrances/exits, which have security systems that monitor vehicle traffic. As a result, Peaceful Valley is considered the safest community in the state. But controversy has come to Peaceful Valley. The suburb’s steering committee has recommended that the community build a swimming pool, tennis court, and meeting room facility on four adjoining vacant lots in the back of the subdivision. Construction cost estimates range from $1.5 million to $2 million, depending on how large the facility will be. Currently, every Peaceful Valley homeowner is billed $100 annu- ally for maintenance, security, and upkeep of Peaceful Valley. About 75% of the residents pay this fee. To construct the proposed recreational facility, each Peaceful Valley household would be expected to pay a one-time fee of $500, and annual fees would increase to $200 based on facility maintenance cost estimates. Objections to the recreational facility come from various quarters. For some, the one-time fee is unac- ceptable; for others, the notion of a recreational facil- ity is not appealing. Some residents have their own swimming pools, belong to local tennis clubs, or oth- erwise have little use for a meeting room facility. Other Peaceful Valley homeowners see the recre- ational facility as a wonderful addition where they could have their children learn to swim, play tennis, or just hang out under supervision. The president of the Peaceful Valley Suburb Association has decided to conduct a survey to poll the opinions and preferences of Peaceful Valley home- owners regarding the swimming pool, tennis court, and meeting room facility concept. 1 If the steering committee agrees to a survey that is accurate to ±5% and at a 95% level of confidence, what sample size should be used? 2 What sample method do you recommend? In mak- ing your recommendation, carefully consider the geographic configuration of Peaceful Valley. Provide the specifics of how each household in the sample should be selected, including what provision(s) to take if a selected household happened to be on vacation or was unwilling to take part in the survey. 3 Should the survey be a sample (of the size you calculated in question 1) or a census of Peaceful Valley homeowners? Defend your choice. Be cer- tain to discuss any practical considerations that enter into your choice. CASE 10.2 Your Integrated Case College Life E-Zine: Sample Decisions This is the eighth case in our integrated case series. You will find the previous College Life E-Zine Cases in Chapters1, 2, 3, 4, 5, 7,and 9. Bob Watts is on the phone with Wesley, one of our hopeful College Life E-Zine owners, discussing the sample size and selection steps of the survey. Wesley has volunteered to talk with Bob about this as he is Case 10.2 317 the one who remembers most about this topic from his undergraduate studies at State U. ―Okay,‖ says Bob, ―we need to make some decisions that will have some important consequences about the generaliz- ability of our survey. As you and the others know, we have an agreement with State University officials to have access to their student data files as long as we provide them with the results of this survey, as they are very interested in partnering with the College Life E-Zine. It could off-load a lot of the State U Web site work that is planned over the next two years. They said they would work with us in any way possible to develop a sample of State U students.‖ Wesley says, ―That’s great! I knew they’d be willing to help us, since my cousin works in the State U Web site tech area, and he told me a year ago that they had so much to do that it might take five years to put it all on State U’s Web site because his area is so under- funded.‖ Wesley continues, ―I actually consulted my old marketing research class notes, and I found that the typical opinion poll has a sample accuracy of from ±3% to ±4%. I will leave it to you to make the recom- mendation, however. And as for the sample selection, I’ll trust it to you as well, but since we are using a tele- phone survey, I found in my notes that random digit dialing is a commonly used technique. But you’re the expert, Bob, so whatever you come up with, we’ll give it strong consideration.‖ Bob Watts says, ―I’ll take all of this under consider- ation and get back to you and the others next week. So long for now.‖ Upon switching off his phone, Bob glances at his calendar and notices that the marketing research intern he hired from from State U—he has jotted her first name down—Lori—will meet with him in three days to begin her five-week rotation in his group. Somewhat devilishly, Bob thinks, ―I think I’ll give this Lori a test. I’ll send her an e-mail with the College Life E-Zine sample decisions that are pend- ing and see what she comes up with for our initial interview.‖ Here is Bob’s e-mail to Lori. To: Lori Baker, Marketing Research Intern From: Bob Watts, Division Manager Subject: Initial Interview Lori: Some time has passed since we met and I hired you as our marketing research intern this semester. You are about to begin your third and last department rotation in the com- pany and into my department. For your initial interview with me on Friday, I am providing you with some informa- tion about a current project, and I would like you to be prepared to discuss with me your recommendations for cer- tain sample decisions that must be made very shortly for the College Life E-Zine project (project proposal attached for your perusal—I have also included my notes with relevant communications, including the most recent one concerning sample size and method with the client group). 1 What is your recommendation as to the sample size for the survey? I suggest that you use Wesley’s telephone conversation comments in deciding on your recommendation. 2 What is your reaction to a random-digit-dialing approach to select the sample of State U students? Consider that we will use a data collection com- pany that can generate random-digit-dialing numbers easily. Does this alter your reaction to random digit dialing to any degree? 3 What if one of our budding College Life E-Zine entrepreneurs is bullish on having us just sample the technical majors at State U, such as computer science, computer and electrical engineering, information systems/decision sciences, computer graphics, and the like? What is your reaction to this sample design and why? 4 State U says it will access its electronic student files to select a sample, but it will only provide us the sample of students based on our instructions as to how to select these students. If I assign you the task of communicating to the State U technical folks how to select the sample, what steps do you propose to tell them to take to effect: aA simple random sample using electronic records? b A systematic sample using the State University Student Directory? Have a good next few days, and I will see you at your interview at 10:00 a.m. on Friday. Your task in analyzing this case is to take Lori’s role and develop answers to each of Bob’s four sampling questions for the College Life E-Zine survey. 311 - 317). <vbk:#page(311)>

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